Dynamical behavior of multi-timescale adaptive threshold model

Abstract

Computational models play a significant role in exploring novel theories to complement the findings of physiological experiments. Various computational models have been developed to reveal the mechanisms underlying brain functions. Particularly, in the development of therapies to modulate behavioral and pathological abnormalities, computational models provide the basic foundations to exhibit transitions between physiological and pathological conditions. Considering the significant roles of the intrinsic properties of the globus pallidus and the coupling connections between neurons in determining the firing patterns and the dynamical activities of the basal ganglia neuronal network, we propose a hypothesis that pathological behaviors under the Parkinsonian state may originate from combined effects of intrinsic properties of globus pallidus neurons and synaptic conductances in the whole neuronal network. In order to establish a computational efficient network model, hybrid Izhikevich neuron model is used due to its capacity of capturing the dynamical characteristics of the biological neuronal activities. Detailed analysis of the individual Izhikevich neuron model can assist in understanding the roles of model parameters, which then facilitates the establishment of the basal ganglia–thalamic network model, and contributes to a further exploration of the underlying mechanisms of the Parkinsonian state. Simulation results show that the hybrid Izhikevich neuron model is capable of capturing many of the dynamical properties of the basal ganglia–thalamic neuronal network, such as variations of the firing rates and emergence of synchronous oscillations under the Parkinsonian condition, despite the simplicity of the two-dimensional neuronal model. It may suggest that the computational efficient hybrid Izhikevich neuron model can be used to explore basal ganglia normal and abnormal functions. Especially it provides an efficient way of emulating the large-scale neuron network and potentially contributes to development of improved therapy for neurological disorders such as Parkinson's disease.